I always felt eldar struggle with long range anti-tank. Bright lances are hot though.
No not in the slightest. Eldar have more D than anyone else. D-Cannon & Heavy D Cannons will put the fear of god, in friendly game most players i play don't even bother taking AV 14 as they know i'm penetrating on a 2+ and a 6 means "Please remove your model".
There's two ways to go Quality and Quantity. I prefer Quantity, Fire Dragons are a particularly poor choice in my opinion, very expensive, poor range and they need a delivery method, Falcon/Wave Serpent.
AV 14 really isn't that common, and the tanks that have them usually are quite expensive and you can deal with AV 14 with Str8 - 1 in 6 hits. If you can kick out 24 shots per turn that should be enough. - See the reaper list i posted. - Quantity over Quality. - Unless it's a WK
Crimson hunters a fine for dealing with Lehman Russ' as they can access their side amour value and they have enough to put some hurt into 14/14/14 tanks.
Regarding the WK it really does solve many of the problems you can get. I don't know why you're worried about an Alpha Strike? They're not really a good idea anymore if you opponent wants to do that, let him/her and sit on a bunch of objectives on the first turn. You do know poisoned and Snipers are on 6's to wound? And you have feel no pain and you can make the thing invisible too. If your opponent still takes in down on turn one, take your hat off to them, that's no easy feat.
Yes i know 50% of time them they'll get first turn but 50% of the time you will.
The WK is actually so good some tournaments/clubs have a no superheavy/gargantuan rule. Invis is so good it's often disallowed/modified.
Regarding catapults and MEQ vs Reapers. The best gun in the world isn't worth a damn if it's 1" out of range you'd find the catapults short range is a problem on the 1st 2 turns (which are more often on not when the game is won or lost).